I know only that the practice, if it ever was a practice in the English-speaking world, derives from the payment to Charon, the ferryman of the underworld, to ferry the deceased across the River Styx (or Acheron), to his destination in the underworld. (One destination was the Elysian Fields, but Greek mythology is full of complexities and variations.) To pay the ferryman, the deceased person's relatives place an obol on each eye of the deceased (or on or in the mouth). Even so, Charon would not deliver the person across the Styx unless the body had had a proper burial.

There are a lot of variations in the story, but the "pennies on a dead man's eyes" were to pay the ferryman. Someone else will have to explain why there is an English phrase for this. SS